Ornstein-Uhlenback type Omega model

doi:10.1007/s11464-016-0521-3

Front. Math. China

2016, Vol. 11

Issue (3) : 737-751 https://doi.org/10.1007/s11464-016-0521-3

RESEARCH ARTICLE

Ornstein-Uhlenback type Omega model

Xiulian WANG¹,Wei WANG^1,^*(

),Chunsheng ZHANG²

1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China

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Abstract

We consider the Omega model with underlying Ornstein-Uhlenbeck type surplus process for an insurance company and obtain some useful results. Explicit expressions for the expected discounted penalty function at bankruptcy with a constant bankruptcy rate and linear bankruptcy rate are derived. Based on random observations of the surplus process, we examine the differentiability for the expected discounted penalty function at bankruptcy especially at zero. Finally, we give the Laplace transforms for occupation times as an important example of Li and Zhou [Adv. Appl. Probab., 2013, 45(4): 1049–1067].

Keywords Omega model Ornstein-Uhlenbeck type Omega model probability of bankruptcy Gerber-Shiu function at bankruptcy occupation time

Corresponding Author(s): Wei WANG

Issue Date: 17 May 2016

Cite this article:

Xiulian WANG,Wei WANG,Chunsheng ZHANG. Ornstein-Uhlenback type Omega model[J]. Front. Math. China, 2016, 11(3): 737-751.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0521-3
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I3/737

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[1]	Ye CHEN, Yingqiu LI, Xiaowen ZHOU. An occupation time related potential measure for diffusion processes[J]. Front. Math. China, 2017, 12(3): 559-582.
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